Manufacturing systems with machine vacations, arbitrary topology and finite buffers

We consider a manufacturing system with finite buffer and arbitrary topology where a machine takes a vacation (i.e. is unavailable for processing due to the processing of secondary jobs or maintenance of machines) of random duration every time the machine becomes idle. To this end, we develop an approximation (analytical) methodology to calculate the throughput of the system using queueing networks together with decomposition, isolation and expansion methodologies. The methodology was tested rigorously covering a large experimental region. We used orthogonal arrays to design the experiments in order to keep the number of experiments manageable. The results obtained using the approximation methodology were compared to simulation results. The t-tests carried out to investigate the differences between the two results showed that the proposed methodology is very accurate as well as robust.